In recent years several major cancer genes have been identified. Typically, mutations in these genes are rare in the population, but they confer a substantially increased risk to carriers. Estimation of their population epidemiologic characteristics, such as relative risks and penetrances, is challenging, primarily because of their rarity. As a result, various novel designs and analytic techniques have been proposed and utilized to estimate these parameters indirectly. The general goal of this revised proposal is to critically evaluate the statistical properties of these methods, to compare different approaches, and to develop new methods as needed. The first aim will focus on penetrance estimation. We will examine the kin-cohort design, when probands have been identified from incident cases, a configuration known to result in upward bias, with a view to developing techniques for bias correction. Also we will study the derivation of penetrance from comparing carrier frequencies in patients with second primaries with patients with first primaries, an approach that does not depend on family histories of cancer. We will endeaver to use these results develop risk predictions that allow for risk adjustment on the basis of known family history of cancer. In the second aim we will build on the design that utilizes first and second primaries to estimate relative risks. The goals here will be to identify and correct the impact of potential survival bias (length biased sampling of second primaries if the gene is associated with survival), to modify analyses for the impact of individuals who qualify as both cases and controls in this study design, and to examine the impact of unknown risk factors that interact with the genotype of interest. All of these aims are motivated by an international study of the genetic epidemiology of melanoma that is currently in progress.